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In the op-amp working principle I was told that if I have a certain input voltage at the non inverting pin, then the inverting pin will also be forced to have that voltage and hence if I attach a feedback impedance to the output, then the output voltage will align itself in such a way that KVL and KCL are conserved along with reflection of a followed voltage at the inverting pin. My question is, why does this reflection of similar voltage at the inverting pin happen depending on the non-inverting pin? Can I also reverse the ideology? That is if I were to have a voltage V0 at the inverting pin and attach a feedback at the non-inverting pin, will it follow the voltage at the inverting pin?

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What you were told is not theoretically correct. You have to change the way o thinking what really happens. It is the feedback loop that can force IN-=IN+ , not IN-=IN+ that makes the loop work.

The condition IN-=IN+ des not happen magically.

Start thinking that \$Vout=A_0(IN_+-IN_-)\$ where \$A_0=10^6\$

This is the IN\Out relation of an open circuit (not in a feedback loop) OPAMP

When you close the OPAMP in a negative feedback loop with resistance \$R_1,R_2 \$ this relation is still valid but the loop will change everithing

When you apply a voltage to the IN+ of the OPAMP, at time \$T=0^+\$ its output will saturate to \$V^+\$(positive rail) as \$IN_+=Vin\$, \$IN_-=0\$ and so \$Vout=10^6(Vin-0)=too much\$.

Then, thanks to the feedback loop \$IN_-\$ will go from \$0\$ to \$V_{out}*\frac{R1}{R_1+R_2}=V^+*\frac{R1}{R_1+R_2}\$.

What happen next is that the value of \$V_{out}\$ will change as the value of \$(IN_+-IN_-)\$ chaged thanks to the loop. As a conseguange the value of \$IN_- \$ will change again and again Vout and \$IN_-\$ again and so on.....

At this point you should understand were we are going, as we have a negative feedback Vout and \$IN_-\$ will change until you reach a point of equilibrium. The point of equilibrium is when you have \$IN_-=IN+\$

This ideology can be reversed but be carful that in the other case the loop becomes a positive one and instead of reducing to \$0\$ the difference \$IN_--IN+\$ this will increase untill you reach another equilibrium point that is in this case \$ V_{out}=V^+\$

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No, reversing the idea results in positive feedback, instead of the negative feedback that's required for the principle you're talking about to hold.

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